An Electromagnetic Band Gap (EBG) antenna is a planar structure which is composed of a cavity and an EBG material. In most applications, the height of the EBG antenna is half wavelength. We present in this paper the conditions to reduce the profile of an EBG antenna to subwavelength values. It could be achieved by using a cavity upper interface which exhibits negative reflection phase. Frequency Selective Surface (FSS) based on Babinet principle, that satisfies this condition, will be described using full wave analysis. These periodic metallic arrays are employed in the design of a low profile EBG antenna which has a directivity of 10 dBi. As this EBG antenna design is similar to a small antenna over an Artificial Magnetic Conductors (AMC) surfaces or High Impedance Surface (HIS), the EBG antenna principle could be a new theory approach for the AMC or HIS. This point is discussed in this paper.